Why am I receiving error messages about singularities in my Simulink model?

Levi - 2020-07-10T13:02:58+00:00

Question: Why am I receiving error messages about singularities in my Simulink model?

I am receiving the following error messages about singularities in my Simulink model:   Derivative of block at time is Inf of NaN. Stopping Simulation. There may be a singularity in the solution. If not, try reducing the step size (either by reducing the fixed step size or by tightening the error tolerances.) I have tried reducing the step size and adjusting tolerances, but I still receive this error message. I have also tried changing solvers, some solvers will just get to one point of the simulation, and hang.

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Expert Answer

Kshitij Singh answered . 2025-12-15

Singularity error messages in Simulink (e.g., "Derivative of state '1' in block ... is not finite" or "There may be a singularity in the solution") typically indicate that the solver encounters infinite (Inf) or undefined (NaN) values during simulation, often causing it to stop.

Common Causes

These errors arise from numerical or modeling issues:

1. Division by zero — A signal reaches zero in a Divide block (or equivalent math), producing Inf/NaN that propagates to an Integrator or other stateful block.
2. Unstable system dynamics — Positive feedback loops, poorly tuned controllers (e.g., high PID gains), or inherently unstable physics cause states to diverge exponentially.
3. Algebraic loops with no convergence — Direct feedthrough loops (no delay/memory) require iterative solving; if inconsistent or singular, they fail.
4. Discontinuities or stiff systems — Abrupt changes (e.g., switches, saturation), very fast transients, or states differing by orders of magnitude make the solver struggle.
5. Initial conditions or step size issues — Bad ICs cause immediate Inf/NaN, or fixed-step size too large misses rapid changes.
6. Input to Integrator/Transfer Fcn becomes infinite — The most common symptom: the derivative explodes.

Troubleshooting Steps

Follow these systematically:

1. Read the exact error message It points to the problematic block (e.g., an Integrator) and time. Start there and trace upstream signals.
2. Check for obvious math issues
   • Search for Divide, 1/x, or trig functions (e.g., tan near π/2).
   • Add small offsets (e.g., divide by x + eps) or Saturation blocks to prevent zero/infinity.
3. Highlight algebraic loops
   • Go to Display > Sample Time > Colors, then Analysis > Algebraic Loops.
   • If present, break them with a Memory or Unit Delay block (introduces one-step delay, often acceptable).
4. Adjust solver settings
   • Switch to variable-step solver (e.g., ode45 or ode15s for stiff systems).
   • Tighten tolerances: Reduce Relative/Absolute tolerance (e.g., to 1e-6).
   • For fixed-step: Reduce step size.
   • Enable "Robust simulation" or check "Solver robustness" options.
5. Inspect signals
   • Scope inputs to the failing block.
   • Log states (Configuration Parameters > Data Import/Export > Log states).
   • Use Solver Profiler (Analysis > Solver Profiler) to identify slow/unstable regions.
6. Simplify the model
   • Disable subsystems one by one.
   • Smooth sharp inputs (add Rate Limiter or low-pass Filter).
   • Scale states if magnitudes vary wildly (e.g., normalize units).
7. Use Simulink Debugger
   • Simulation > Debug > Debug Model.
   • Step through to where NaN appears.

Quick Fixes That Often Work

• Add a small bias to avoid zero division.
• Insert a Memory block in feedback paths.
• Filter noisy or step-like references.
• Reset Integrator initial conditions.

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